Range of `f(theta)=cos^2theta(cos^2theta+1)+2 sin^2theta` is
Range of `f(theta)=cos^2theta(cos^2theta+1)+2 sin^2theta` is
A. `[3//4,1]`
B. `[3//16,1]`
C. `[3//4,7//4]`
D. `[7//4,2]`
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Correct Answer - D
`f(theta)=cos^2theta(cos^2theta+1)+2sin^2theta`
`=cos^4theta+cos^2theta+sin^2theta+sin^2theta`
`=cos^4theta+1+1-cos^2theta`
`=(cos^2theta-1/2)^2+2-1/4`
`=(cos^2theta-1/2)^2+7/4`
`f_("min")=7/4`
`f_("max")=1/4+7/4=2`
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